Question

a spinner has 4 equal - sized sections labeled a, b, c, and d. it is spun and a fair coin is tossed. what is the probability of spinning \c\ and flipping \heads\?
$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$

Explanation:

Step1: Calculate the probability of spinning "C"

The spinner has 4 equal - sized sections. The probability of spinning "C" is \(P(C)=\frac{1}{4}\) since there is 1 favorable outcome (section C) out of 4 total outcomes.

Step2: Calculate the probability of flipping "heads"

A fair coin has 2 possible outcomes (heads or tails). The probability of flipping "heads" is \(P(H)=\frac{1}{2}\) since there is 1 favorable outcome (heads) out of 2 total outcomes.

Step3: Use the multiplication rule for independent events

Since spinning the spinner and flipping the coin are independent events (the outcome of one does not affect the outcome of the other), the probability of both events occurring is \(P(C\cap H)=P(C)\times P(H)\).
Substitute \(P(C)=\frac{1}{4}\) and \(P(H)=\frac{1}{2}\) into the formula: \(P(C\cap H)=\frac{1}{4}\times\frac{1}{2}=\frac{1\times1}{4\times2}=\frac{1}{8}\)

Answer:

\(\frac{1}{8}\) (the first option)